This is an interesting question, because the Gemara above 109a; 8 lines from the top; says "I can say 'She'eiro' means the father?" so why does Rashbam 115a DH v'HaAv not mention She'eiro to show that the Av comes before the Ach?

My initial reaction is that Rashbam holds that we pasken that from "She'eiro" we derive that the husband inherits his wife, so we cannot learn from the same word that the father inherits his children. I have not yet found a strong proof that we pasken that from She'eiro we learn that the husband inherits his wife, but the fact that the Gemara cites twice (109b and 111b) the Braisa that we learn from She'eiro that the husband inherits his wife, suggests that this is a strong Limud.

I have now found, bs'd, some Rishonim who derive from "v'Ha'avarta" that the father preceeds the brothers to inherit his son, and from "She'eiro" that the husband inherits his wife, and I argue that the Rashbam also learns this way, which is why he only mentioned v'Haavarta in 115a.

1) The Rif here, right at the beginning of the 8th chapter in the Gemara (top 52a in Rif pages) learns from v'Haavartem that the father comes before the brothers. Then, nearer the end of 52a, he writes "She'eiro Zu Ishto" which teaches that the husband inherits his wife. I argue that since She'eiro teaches that the husband inherits his wife, it cannot also teach that the father comes before the brothers, so the latter has to be derived from v'Haavartem.

2) The Rosh, at the beginning of the chapter, goes the same way as the Rif, and cites the above 2 droshos. That is not unusual, since the Rosh very often cites the Rif word for word. However, there is a Chidush here in the very first comment of the Pilpula Charifta on the Rosh in this chapter. He writes that it appears, from the fact that the Rosh cites "She'eiro" as the source that the husband inherits his wife, that the husband inherits his wife according to Torah law. Pilpula Charifta cites a couple more sources for this idea.

3) The Tosfos Yomtov (who was also the author of Pilpula Charifta) writes on the first Mishnah in the 8th chapter near end of DH v'HaIsh that "She'iro Zu Ishto" is originally stated to tell us that if the husband is a Cohen he still must become Tamei in order to bury his deceased wife. After we learnt that, we then have a Binyan Av which teaches us that wherever the Torah states "She'eiro" this also means the wife. So this is another source that Mideoraisa the husband inherits his wife. This is why Rashbam omitted She'eiro when referring to the father coming before the brothers, because it is needed for a Torah teaching that the husband inherits his wife.

Why did the Rif and the Rashbam both learn from veHa'avartem that the father inherits before the brothers?:-

Above, I suggested that the Rif and the Rashbam are following the same way in learning the droshos here (by the way, the Rashbam was born about 70 years after the Rif, but I believe that Rashbam did not see the works of the Rif, since Rashbam lived in France and the Rif in North Africa and Southern Spain and there was not communcation between the two centers, so they probably reached their conclusions independently).

The question is:- why did the Rif decide that the conclusion of the Gemara is that the Din that the father inherits before the brothers is derived from veHaavartem and the Din that the husband inherits his wife is learnt from "Sheeiro Zu Ishto" even though there are other verses also mentioned in the Gemara as the source for these Dinim?

I want to suggest 2 simple reasons for this:-

1) The Rif learnt that the Droshos that are cited at a later stage of the Gemara have a stronger authority in deciding the Halachic conclusion. What is stated nearer the conclusion of the sugya suggests that it is closer to the Halachic conclusion. Sheeiro Zu HaAv comes on 108b whilst veHaavartem comes on 109a, and Sheeiro Zu Ishto comes even later on 109b and 111b.

2) The Drosho that veHaavartem teaches that the father preceeds the brothers was stated by Rabbi Yishmael the son of Rabbi Yosi on 109a, whilst the Drosho that this same Din is derived from Sheeiro Zu HaAv was said by an anonymous Tana on 108b, so R. Yishmael beRebbi Yosi's drosho has more authority since it was said by a known, significant Tana.

Rashbam 115a writes that veHaavartem teaches that the father comes before the brothers, which means he does not derive this Din from Sheeiro Zu HaAv. This suggests that he lesarns Sheeiro Zu Ishto, which is the same as the Rif.

Dovid Bloom

The Rif and Rashbam paskened that Sheeiro teaches that the husband inherits the wife because RaMa of Panu writes that "Tanu Rabanan" is stronger than "Tanya":-

Here is another idea to explain why the Rif and Rashbam wrote that we learn from veHaavartem; and not from Sheeiro; that the father takes precedence to his son's brothers to inherit the son.

1) I noticed that on 111b the Din that "Sheeiro Zu Ishto" is preceded by the words "Tanu Rabanan" whereas on 108b the Din that "Sheeiro Zeh HaAv" is preceded by the word "Tanya".

I found, bs'd, in Teshuvos Rama of Panu [who lived in Italy 1548-1620] #25, that he was asked what is the difference between Tanya and Tanu Rabanan? He writes that he himself was in doubt about this for a long time and he asked Chachamim but nobody had an answer for him. But then he thought about the Mishnah Eduyos 5:7 where Akavya ben Mehallel taught that it is better to hear a Halacha from many Chachamim than merely from an individual. Rama of Panu writes that one can learn from this what the significance of the words "Tanu Rabanan" is. It means "the Rabbis taught". Many Rabbis taught this. In contrast "Tanya" simply indicates that an individual taught the Braisa in the Beis HaMidrash. The individual Chacham cited the Braisa that he had heard and it was accepted by others. Tanu Rabanan is better than Tanya because Tanu Rabanan means it is a Braisa that is well-known and said by everyone.

2) If we now apply the idea of RaMa of Panu to our Sugya I think it adds a lot to our understanding. On 108b we have an individual Tana citing a Braisa that Sheeiro means the father. But on 111b we have a Braisa that the Rabbis taught that Sheeiro means "his wife". The latter teaching is something that everyone knows about. It is more authoritative than 108b. This is why the Rif cites the Braisa of 111b and once we know that Sheeiro Zu Ishto it follows that we cannot say Sheeiro Zu HaAv so we have to learn that the father takes precedence to the brothers from veHaavartem. This is also why Rashbam 115a cites veHaavartem and not Sheeiro.

Dovid Bloom